Question

Решите пожалуйста, срочно надо. Заранее спасибо)
1)sin15°-sin75°
2)cos15°+cos165°
3)sin2П\5+sinП\5
4)sinП\6-sinП\9

Answer 1

1)sin15°=sin(45-30)=sin45*cos30-cos45*sin30=√2/2(sin45)*√3/2(cos30)-√2/2(cos45)*1/2(sin30)=√6/4-√2/4=(√6-√2)/4
sin75°=sin(45+30)=sin45*cos30+cos45*sin30=√2/2(sin45)*√3/2(cos30)+√2/2(cos45)*1/2(sin30)=√6/4+√2/4=(√6+√2)/4
(√6-√2)/4-(√6+√2)/4=(√6-√2-√6-√2)/4=-2√2/4=-√2/2
2)cos15°+cos165°=
cos15°=cos(45-30)=cos45*cos30-sin45*sin30=√2/2(cos45)*√3/2(cos30)-√2/2(sin45)*1/2(sin30)=√6/4-√2/4=(√6-√2)/4
cos165=cos(90+75)=-sin75=-sin(45+30)=-(sin45*cos30+cos45*sin30)=-(√2/2(sin45)*√3/2(cos30)+√2/2(cos45)*1/2(sin30))=-(√6/4+√2/4)=(-√6-√2)/4
(√6-√2)/4+(-√6-√2)/4=(√6-√2-√6-√2)/4=-2√2/4=-√2/2
3)